Best Known (70−16, 70, s)-Nets in Base 8
(70−16, 70, 4096)-Net over F8 — Constructive and digital
Digital (54, 70, 4096)-net over F8, using
- net defined by OOA [i] based on linear OOA(870, 4096, F8, 16, 16) (dual of [(4096, 16), 65466, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(870, 32768, F8, 16) (dual of [32768, 32698, 17]-code), using
- 1 times truncation [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(870, 32768, F8, 16) (dual of [32768, 32698, 17]-code), using
(70−16, 70, 24387)-Net over F8 — Digital
Digital (54, 70, 24387)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(870, 24387, F8, 16) (dual of [24387, 24317, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(870, 32768, F8, 16) (dual of [32768, 32698, 17]-code), using
- 1 times truncation [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(870, 32768, F8, 16) (dual of [32768, 32698, 17]-code), using
(70−16, 70, large)-Net in Base 8 — Upper bound on s
There is no (54, 70, large)-net in base 8, because
- 14 times m-reduction [i] would yield (54, 56, large)-net in base 8, but